I know about the rain and mud thing!! When we had a westie the only time he would dig outof the yard was when it had been raining and the ground was soggy!!!
These are some solutions I have used. Hopefully one of them will be doable for you.
You can use tent stakes or shishkebob skewers (I used 18 inch metal skewers shaped with a round end that (bent so that it was not quite a complete circle). I hooked the round end over the bottom wires of my chain link fence then stuck the skewers the 18 inches into the ground. You have to put them pretty close together though, about 4 inches apart or closer. That worked pretty good, except when the ground got really soupy and soft, then they could just push them aside and go through.
In my dog yard to stop the digging in general and around the fence I covered the ground with plastic mesh that's kind of like chicken wire. I used landscaping staples to hold it down. The grass grows right through it and eventually you can't see it. It has worked really well.
How about putting some of that or chicken wire or plastic mesh flat on the ground right next to the fence and out about six to eight inches. Be sure to secure it with landscaping staples or something. Then whenever they try to dig they hit the chicken wire and can't do it. I prefer the plastic, because I was afraid the chicken wire might eventually rust and break and then there would be sharp edges, that is why I used the plastic. I bought it at Walmart in the gardening section. It comes in a roll. Here's a link where someone used it on their balcony and posted pictures, so you can see what it looks like.
http://www.yorkietalk.com/forums/sho...stic+mesh%2 2 I have also posted pictures here
http://www.yorkietalk.com/forums/sho...c+chicken+wire
Hope this helps!